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The image provided includes instructions for a project based on **Critical Path Method (CPM)**. This method involves determining the **critical path** in a directed graph (as shown in the diagram), which is crucial for understanding the **project duration** and identifying the tasks that cannot be delayed without affecting the project's total duration.

To break it down:
1. **Nodes (circles)** represent different tasks or events.
2. **Edges (arrows)** between the nodes represent the tasks, along with their durations (numbers next to the arrows).
3. The task is to calculate:
   - **Project duration**, which is the time needed to complete the project.
   - **Critical path**, the longest path from the start node (1) to the end node (6), where any delay will impact the project.

### Approach:
- List all possible paths from **node 1** to **node 6**.
- Calculate the total duration for each path by adding the values on the edges.
- The longest path gives the **critical path** and thus the **minimum project duration**.

Let me analyze the diagram and determine the critical path and project duration.The analysis of the graph reveals the following:

- Path 1: \(1 \to 2 \to 4 \to 6\) has a total duration of **8 units**.
- Path 2: \(1 \to 3 \to 5 \to 6\) has a total duration of **9 units**.
- Path 3: \(1 \to 2 \to 5 \to 6\) also has a total duration of **9 units**.

### Result:
- The **critical path** is either **Path 2** or **Path 3** (both have a duration of **9 units**).
- Therefore, the **project duration** is **9 units**.

Would you like a more detailed breakdown of the steps or explanation on the critical path method?

Here are five follow-up questions to consider:
1. How can slack times be calculated for non-critical paths?
2. What happens if a task on the critical path is delayed?
3. How can this method be applied in real-world project management?
4. What are the differences between CPM and PERT (Program Evaluation Review Technique)?
5. How does one manage resources for tasks on the critical path?

**Tip:** In critical path analysis, tasks not on the critical path often have "float" or "slack," meaning they can be delayed without affecting the project's completion time.

Indicar duración del proyecto y camino crítico usando el diagrama de red proporcionado.

Resuelve un problema de programación de camino crítico utilizando el diagrama de red proporcionado. Aprende a identificar el camino crítico y calcular la duración total del proyecto aplicando conceptos de teoría de grafos y CPM. Adecuado para estudiantes universitarios de ingeniería y gestión de proyectos.

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